Under what condition will the equality : `vec A xx vec B = vec A . vec B` hold good ?

What is the condition for vec A+vec B=vec A-vec B?

What is the angle between (vec A+ vec B) and (vec A xx vec B) ?

If vec A and vec B are two vectors satisfying the relation vec A cdot vec B = |vec A xx vec B| . Then the value of |vec A - vec B| will be :

Under what condition |vec(A)+vec(B)| = |vec(A)|+|vec(B)| holds good?

Three vectors vec a, vec b and vec c satisfy the condition vec a + vec b + vec b + vec c = vec 0 .Evaluate the quantity mu = vec a * vec b + vec b * vec c + vec c * vec a , if | vec a | = 1 | vec b | = 4 and | vec c | = 2

What is the value of (vec(A) + vec(B)) .(vec(A) xx vec(B)) ?

Given two orthogonal vectors vec(A) and vec(B) each of length unity . Let vec(P) be the vector satisfying the equation vec(P) xx vec(B) = vec(A) - vec(P) . Then (vec(P) xx vec(B)) xx vec(B) is equal to .

Show that (vec(A) - vec(B)) xx (vec(A) +vec(B)) = 2(vec(A) xx vec(B))

Solve the following equation for the vector vec p; vec p xx vec a+(vec p. vec b)vec c=vec b xx vec c where vec a ,vec b,vec c are non zero non coplanar vectors and vec a is neither perpendicular to vec b non to vec c hence show that (vec p xx vec a+([vec a vec b vec c])/(vec a*vec c) vec c) is perpendicular vec b-vec c.